Termination at low conversion

Most in depth studies of termination deal only with the low conversion regime. Logic dictates that simple center of mass diffusion and overall chain movement by reptation or many other mechanisms will be chain length dependent. At any instant, the overall rate coefficient for termination can be expressed as a weighted average of individual chain length dependent rate coefficients (eq. 20)  

Mahabadi and O Driscolh considered that segmental motion and center of mass diffusion should be the dominant mechanisms at low conversion. I hey analyzed data for various polymerizations and proposed that should be dependent on chain length such that the overall rate constant obeys the expression  

Various expressions have been proposed for estimating how the overall rate coefficient kt and the individual rate coefficients vary with the chain lengths of the reacting species,simple relationships of the following fomis are the most often applied  

Flowever, it has been pointed out that the value of A to in the expressions eqs. 25-23 should not be confused with the small radical fe, , rather, the value of represents the termination rate constant of a single unit chain if the implied diffusion mechanism was the rate-determining process. 

Recent work has allowed values of A, and a for bulk polymerization in dilute solution to be estimated. This work suggests values of At =A, 1x10 M and a 0.15-0.25 for both MMA and Some values of A, and a for S and 

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Deviations resulting from the diffusion control of termination at low conversions of monomer to polymer are the relatively weak effects discussed in the preceding subsection. By contrast, changes in reaction rate resulting from hindered diffusion at high conversions are very important in most radical polymerizations. Figure 6-3 shows rate curves for the polymerization of methyl methacrylate in benzene at 50°C [17]. At monomer concentrations less than about 40 wt % in this case, the rate is approximately as anticipated from the standard kinetic scheme described in this chapter. Rp decreases gradually as the reaction proceeds and the concentrations of monomer and initiator are depicted. 

Initial Rate Method For reversible reactions, we use a modified differential method—the initial rate method. In this case, a series of experiments are conducted at selected initial reactant compositions, and each run is terminated at low conversion. From the collected data, we calculate (by numerical differentiation) the reaction rate at the initial conditions. Since the reaction extent is low, the reverse reaction is negligible, and we can readily determine the orders of the forward reaction from the known initial compositions. The rate of the reversible reaction is determined by conducting a series of experiments when the reactor is charged with selected initial product compositions. The initial rate method is also used to determine the rates for complex reactions since it enables us to isolate the effect of different reactants. 

In order to improve hydrolytic stability chlorine groups have been replaced by such moieties as alkoxy, aryloxy and amine groups. Most of the early modifications were cross-linked and thus intractable and difficult to characterize. For this reason little progress was made until Allcock and Kugel (1965) disclosed methods of termination at low conversions to give a material that remained soluble. 

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